1. Tangential Speed When an object moves in a straight path, its average speed is calculated using the following formula: speed = distance / time When an object travels in a circle, the distance traveled is along the circumference of the circle C = 2πr The tangential speed is the amount of distance traveled along the circumference over the time elapsed 1 Circular and Orbital Motion

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3. An ant is at the edge of a turntable when it starts to spin. At full speed, the turntable rotates one time in two seconds. If the turntable has a radius of 5 cm, what is the tangential speed of the ant? If the ant were to move 2 cm away from the center, would the tangential speed change? If so, how much? 0.16 m/s 3 Yes, 0.063 m/s

4. Centripetal Force An object moves in a circular path because of a centripetal force that is acting on the object. Centripetal force– a force perpendicular to the circular motion of an object and directed toward the center of the circle When an object moves in a circular path, its tangential speed remains constant. This type of motion is called uniform circular motion (UCM). 4

5. Each of these objects have centripetal forces acting on them. Reflect on the types of traditional forces that are making these objects move in circular paths. These forces in this context are centripetal forces. A centripetal force is NOT a new type of force. It is simply a traditional force that is now making an object maintain a circular path. 5

6. If centripetal forces go inward, why do you feel like you are being pulled outward when a car makes a sharp turn? The force is exerted on the car, helping it maintain a circular path. However, the car and the driver want to continue in a straight line because of their respective interias. Inertia is what makes the driver feel like the door is pushing on him. Does the water fall out of the bucket? Why or why not? 6

7. Centripetal forces, like all forces, cause objects to accelerate. Reflect on the definition of acceleration. It is simply the rate at which an object’s velocity changes. This object’s speed is constant but its velocity is changing. Why? Its direction is changing Since its direction is changing, its velocity is changing. Therefore, it experiences an acceleration caused by a force. Both the force and the acceleration are pointed inward. 7

8. a c = centripetal acceleration (m/s 2 ) v t = tangential speed (m/s) r = radius of circle (m) ΣF c = net centripetal force (N) m = mass (kg) Both are vector quantities pointed toward the center of the circle. 8

9. A 0.150-kg ball on the end of a 1.10-m cord is swung in a vertical circle. What is the minimum speed the ball must have at the top of its arc so that the ball continues moving in a circle? What would be the tension of the cord at the bottom if the ball is traveling twice the speed of the 1 st part? 3.28 m/s 7.34 N 9

10. A 1000-kg car rounds a curve on a flat road of radius 50 m at a speed of 14 m/s. Assuming the pavement is dry (μ s = 0.60), will the car follow the curve or will it skid? What if the pavement was covered with ice (μ s = 0.25)? Skid b/c friction is not sufficient follow the curve b/c friction is sufficient 10

11. Newton’s Law of Gravitation. Newton’s most famous contribution to physics was his 3 laws of motion. But he also studied how gravity works. He pondered the following mystery… why, if an apple falls out of a tree toward the Earth, doesn’t the moon also fall toward the Earth. 11

12. It turns out that it is attracted, but there are two types of motion working together: 1. An orbiting object has inertia which causes it to move in a straight line. 2. An orbiting object also experiences gravity which is an attractive force toward the Earth. Together, these two types of motion create orbital (or satellite) motion. Satellites can be natural like the moon or artificial like a piece of machinery that transmits your TV signal. 12

13. G = gravitational constant = 6.67 x 10 -11 Nm 2 /kg 2 m 1 = mass #1 (kg) m 2 = mass #2 (kg) r = distance between centers of mass (m) Newton’s Law of Universal Gravitation applies between any two objects that have mass regardless of size. 13

14. What is the gravitational force between the Earth and the Sun? Use the table on the front cover of your book for the necessary information. A 50-kg woman sits 0.5 meters away from a 75-kg man. What is the gravitational force between the two people? 3.55 x 10 22 N 1 x 10 -6 N 14

15. F g = Gm 1 m 2 /r 2 mg = Gm E m/r E 2 g = gravitational acceleration (m/s 2 ) m E = mass of Earth (kg) r = radius of Earth (m) To find out the acceleration of something falling on the surface of Earth, Newton’s 2 nd Law can be applied. What that means: Objects fall at slightly different rates of acceleration at different elevations (not always 9.8 m/s 2 on Earth) The mass of the object falling is irrelevant 15

16. What is an object’s gravitational acceleration at the summit of Mt. Everest (8850 m) and the bottom of the Mariana Trench(-10 994 m) Consult your textbook for the relevant measurements about the Earth. 9.77 m/s 2 9.83 m/s 2 16

17. Orbital Motion Satellites are objects that orbit the Earth. They are given a tangential speed that counteracts the effects of gravity so that they maintain a circular path. Every altitude requires a specific tangential speed that will allow the satellite to maintain its circular orbit. 17

18. People that are in orbit experience “apparent weightlessness”. It is not “actual weightlessness” because the satellite and occupants are still under the effects of gravity. There is NO normal force pushing back on them giving them a sense of having weight. It is analogous to the apparent weightlessness felt by occupants of an elevator in freefall. 18

19. What would be the gravitational acceleration of the space station that orbits at an altitude of 4500 km? How fast would it have to go to maintain its orbit? Earth Why do the occupants experience weightlessness if they are under the effects of gravity? 3.37 m/s 2 6055 m/s they are in constant freefall 19

20. We can prove mathematically that the mass of the satellite is irrelevant to the speed necessary for it to maintain orbit. GM S M E /r 2 = M S v 2 /r GM E /r 2 = v 2 /r GM E /r = v 2 20 The highest satellites are 22,000 miles above the Earth’s surface (they move slower than the Earth’s rotation) Satellites that have speeds that match the spin of the Earth are called geosynchronous satellites. Why do they all have to be at the same altitude? What would that altitude be?

21. 21 Calculate the speed of a satellite moving in stable circular orbit about the Earth at an altitude of 3600 km. At what altitude would a satellite require a tangential speed of 7800 m/s? 6322 m/s 137 km

22. Astronauts train in a similar weightless environment in a “zero g” airplane. Plane makes large parabolic turns with 30-s intervals of weightlessness. What sensation do they experience at the bottom of the curve? 22

23. Simulated Gravity in Space Physicists have theorized that floating (NOT orbiting) space stations can be made to simulate gravity for the occupants inside These spacecraft are not significantly influenced by any type of gravitational force – a simulated gravity is created by rotating the space station around its own axis 23

24. At what rotational speed (RPM) must a cylindrical spaceship rotate if occupants are to experience simulated gravitational acceleration like that of Earth? Assume the spaceship’s radius is 500 m. 1.34 RPM 24

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